1. Field of the Invention
This invention relates to a process simulation for simulating a manufacturing process of a semiconductor device by means of a computer, and more particularly to a method of estimating the shape of a chemically amplified resist by a computer simulation.
2. Description of the Related Art
In a simulation of a manufacturing process of a semiconductor device, that is, a process simulation, a computer is used to simulate various processes upon manufacturing of a semiconductor device such as a lithography process, an ion implantation process and a diffusion process. The shapes of various device portions, a concentration distribution of an impurity in the device, and the like can be estimated through the process simulation without actually manufacturing a semiconductor device. Particularly, in a simulation of a lithography, it is calculated what shape a photo resist after exposure and development will have when exposure using a mask pattern given in advance is performed on the photo resist applied to a semiconductor substrate.
Conventionally, as a method of calculating and estimating a two-dimensional shape of a photo resist at a high speed in the field of a lithography simulation, a method which uses calculation of a light intensity distribution on a wafer is disclosed in Burn Jen Lin, IEEE Trans. on Electron Devices, Vol. ED-27, No. 5, pp.931-938, 1980, and this method is employed popularly. In the method which uses calculation of a light intensity distribution on a wafer, light intensity distribution I(x, y) on a wafer is calculated in accordance with the following equation of Hopkins:                               I          ⁢                      (                          x              ,              y                        )                          =                  ∫                      ∫                                          S                ⁡                                  (                                      p                    ,                    q                                    )                                            ⁢                                                "LeftBracketingBar"                                      ∫                                          ∫                                                                        F                          ⁡                                                      (                                                                                          x                                o                                                            ,                                                              y                                o                                                                                      )                                                                          ⁢                                                  K                          ⁡                                                      (                                                                                          x                                -                                                                  x                                  o                                                                                            ,                                                              y                                -                                                                  y                                  o                                                                                                                      )                                                                          ⁢                                                  exp                          ⁡                                                      (                                                                                          i                                ⁢                                                                  xe2x80x83                                                                ⁢                                2                                ⁢                                π                                                                                            λ                                ⁡                                                                  (                                                                                                            px                                      o                                                                        +                                                                          qy                                      o                                                                                                        )                                                                                                                      )                                                                          ⁢                                                  ⅆ                                                      x                            o                                                                          ⁢                                                  ⅆ                                                      y                            o                                                                                                                                "RightBracketingBar"                                2                            ⁢                              xe2x80x83                            ⁢                              ⅆ                                  xe2x80x83                                ⁢                p                            ⁢                              xe2x80x83                            ⁢                              ⅆ                                  xe2x80x83                                ⁢                q                                                                        (        1        )            
where x, y are two-dimensional coordinate values representative of a point on the wafer; S, which is a function representative of an effective light source, is a function representative of the intensity of light at a point (p, q) on the light source; F is a function representative of a mask transmittance at a point (x0, y0) on the mask, K a pupil function, xcex an exposure light wavelength, i the imaginary unit (i2xe2x89xa6xe2x88x921), and xcfx80 the circular constant.
Pupil function K above is represented by       K    ⁢          (              x        ,        y            )        =                    K        o            ⁢              (                  x          ,          y                )              ⁢          exp      ⁢              (                                            2              ⁢              π              ⁢                              xe2x80x83                            ⁢              i                        λ                    ⁢                                                    fNA                2                            ⁢                              (                                                      x                    2                                    +                                      y                    2                                                  )                                                    a              2                                      )            
where f is a focus value, NA a numerical aperture, and a an aperture diameter. K0(x, y) is represented by             K      o        ⁡          (              x        ,        y            )        =      {                            1                                      [                                                            (                                                            x                      2                                        +                                          y                      2                                                        )                                /                                  a                  2                                            ≤              1                        ]                                                0                                      [                                                            (                                                            x                      2                                        +                                          y                      2                                                        )                                /                                  a                  2                                             greater than               1                        ]                              
Then, based on light intensity distribution I(x, y) determined in accordance with equation (1) above, a photo resist shape is calculated from a contour (isointensity line) of the light intensity distribution at light intensity threshold value Ith.
FIG. 1 is a flow chart illustrating a procedure of the conventional lithography simulation described above. First in step 51, light intensity distribution I(x, y) of a two-dimensional pattern on a wafer is calculated, and then in step 52, a two-dimensional resist shape is calculated from a contour obtained by cutting light intensity distribution I(x, y) at light intensity threshold value Ith.
Meanwhile, Japanese Patent Laid-Open Application No. 6-045424 (JP, 06045424, A) discloses a method wherein resolution rates of a resist corresponding to various exposure amounts are determined in advance by an experiment, and a resolution rate at each portion of the resist is determined from a result of a simulation regarding an image-formation strength of light to estimate the shape of the photo resist after development. Japanese Patent Laid-Open Application No. 6-342746 (JP, 06342736, A) discloses another method wherein an influence of reflection from a base substrate is taken into consideration to simulate the shape of a resist.
By the way, as refinement of the pattern size of a semiconductor device proceeds in recent years, the wavelength of light used for exposure becomes short, and this gives rise to such a problem that a conventional photo resist is not sufficiently high in resolution and in sensitivity. As a countermeasure for the problem, a chemically amplified resist containing a photosensitive agent (i.e., an acid generator) and a dissolution inhibitor (or a cross linking agent) has been developed. Where the resist is a positive resist, a dissolution inhibitor is used, but where the resist is a negative resist, a cross linking agent is used. In a lithography step in which a chemically amplified resist is used, a photosensitive agent is dissolved to generate acid by exposure to light, and in a later heating process (post-baking process), the acid diffuses into the resist and simultaneously a decomposition reaction of the dissolution stopping agent or a cross linking reaction of the cross linking agent by a catalytic action of the acid occurs. Where a chemically amplified resist is used, a high sensitivity can be achieved by utilizing a catalytic reaction, and since the concentration of the photosensitive agent can be reduced, the transparency is augmented and augmentation of the resolution can be achieved.
Such a conventional method described above, however, is disadvantageous in that, when a shape of such a chemically amplified resist as described above is simulated, since an influence of acid diffusion upon the post-baking process is not taken into consideration, the calculation accuracy of a shape is low particularly when the type of the photo resist changes.
It is an object of the present invention to provide a shape estimating method by which, also where a chemically amplified resist is used, the shape of the resist can be estimated accurately by a simulation.
The object of the present invention described above is achieved by a method for estimating a shape of a chemically amplified resist by a computer simulation, comprising the steps of calculating diffusion of a catalyst species in the chemically amplified resist upon a post-baking process by approximation with a Gaussian distribution, calculating a light intensity distribution on the chemically amplified resist upon exposure to light, correcting the light intensity distribution with the Gaussian distribution, and performing calculation of the shape of a two-dimensional pattern of the chemically amplified resist based on the corrected light intensity distribution.
Here, the catalyst species typically is an acid which acts as a catalyst upon a dissolution stopping agent or cross linking agent upon the post-baking process of the chemically amplified resist.
In particular, in the present invention, it is assumed that a catalyst species such as an acid diffuses isotropically in the resist, and this isotropic diffusion is approximated with a Gaussian distribution. A two-dimensional isotropic Gaussian distribution is preferably used as the Gaussian distribution approximating the diffusion process of the catalyst species. Such a Gaussian distribution is characterized by a single parameter representative of a degree of broadening of the distribution except two-dimensional coordinates of the position of a maximal point. Here, this single parameter is set to diffusion length dl. Diffusion length dl is a parameter which depends upon the type of the chemically amplified resist, the time of the post-baking process, the temperature and so forth, and preferably, diffusion length dl is determined in advance based on actual measurements.
Further, in the present invention, if optical proximity effect correction (OPC) is performed, then the correction of the mask pattern, the calculation of the light intensity distribution based on the corrected mask pattern and the correction of the calculated light intensity distribution with the Gaussian distribution should be repeated until a desired resist pattern shape is obtained.
According to the present invention, since, when a simulation of a lithography process is performed, a distribution of a diffusion species is approximated with a Gaussian distribution based on measurement data of dimension linearity of a one-dimensional L/S (line-and-space) pattern of a chemically amplified resist and/or like data and the light intensity distribution on the resist is corrected with the Gaussian distribution and then shape distribution of a two-dimensional pattern is performed based on the corrected light intensity distribution, also where a chemically amplified resist is used, a photo resist shape can be determined with a high degree of accuracy.
The above and other objects, features, and advantages of the present invention will become apparent from the following description referring to the accompanying drawings which illustrate examples of the preferred embodiments of the present invention.